Question: The first term in a geometric series is $5$ and the common ratio is $2$. Find the sum of the first $10$ terms in the series.
Explanation: This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for $ n$, $ a$, and $C r$. All we need to do is plug them in the formula. We are given that ${n=10}$, ${a=5}$, and $C{r=2}$ : ${S_n}=\dfrac{ 5(1-C 2^{{10}})}{1-C 2}$ Evaluating the expression in the calculator, we get that $S_n=5115$. In conclusion, the sum of the first $10$ terms in the series is $5115$.